Triangle ABC with vertices A(4, -6), B(2, -8), and C(-10, 4) is dilated by a scale factor of 2 to obtain triangle A'B'C Which statement best describes triangle A'B'C it is similar to triangle ABC and has coordinates A'(2,-3), B'(1,-4), and C'(-5, 2). It is similar to triangle ABC and has coordinates A'(8,-12). B'(4, -16), and C'(-20, 8). It is congruent to triangle ABC and has coordinates A'(2, -3), B'(1,-4), and C'(-5, 2). It is congruent to triangle ABC and has coordinates A'(8, -12), B'(4,-16), and C'(-20, 8).

[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]

The probability of randomly selecting two jelly beans in succession without replacement is;

0.0857

The jar contains 50 jellybeans.

Thus; N = 50

The individual berries include;

5 lemon

10 watermelon

15 blueberry

20 grape

Probability of first being a jelly bean = 15/50

Probability of second being jelly bean = 14/49

Thus,probability of selecting 2 jelly beans in succession without replacement is =

15/50 × 14/49 = 0.0857

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Answer:

Step-by-step explanation:

(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:

  A = x(12 -2x)

This equation describes a parabola that opens downward. It has zeros at ...

  x = 0

  12 -2x = 0 . . . . x = 6

The maximum area is halfway between these zeros, at x=3.

The maximum area is obtained when the depth is 3 inches.

__

(b) For an area of at least 16 square inches, we want ...

  x(12 -2x) ≥ 16

  x(6 -x) ≥ 8 . . . . . divide by 2

  0 ≥ x² -6x +8 . . . . subtract the left side

  (x -4)(x -2) ≤ 0 . . . factor

The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.

At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.

The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.

Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.

Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.

To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.

For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.

In conclusion,

The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.

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Answer:

60060 different ways that teams can be chosen

Step-by-step explanation:

Given data

employees n  = 14

team = 3

each project employees

n(1) =  8

n(2) = 3

n(3) = 3

to find out

how many different ways can the teams be chosen

solution

we know according to question all employees work on a team so

select ways are = n! / n(1) ! × n(2) ! × n(3)     ....................1

here  n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1

and n(1)! = 8! =  8 ×7 ×6 ×5 ×4 × 3× 2× 1

n(2)! = 3! =  3× 2× 1

n(3)! = 3! =  3× 2× 1

so now put all these in equation 1 and we get

select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) ×  ( 3× 2× 1)

select ways are =  2162160 / 36

select ways are = 60060

60060 different ways that teams can be chosen

Answer:

60060

Step-by-step explanation:

#copyright

Answer:

The next two terms after a1 is

-6 and then 18

Step-by-step explanation:

Geometric sequence means your pattern for the terms is multiplication by the same number.

So a1 is the first term and r is your common ratio.

The common ratio is what you are multiplying by each time to figure out the next term.

So the geometric sequence goes like this:

a1 ,  a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....

So anyways you have

first term a1=2

second term a2=2(-3)=-6

third term a3=-6(-3)=18

And so on...

[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{\sqrt{4}}{\sqrt{9}}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=\frac{2}{3} \end{cases}\implies 8=s_1\left( \frac{2}{3} \right)^{6-1} \\\\\\ 8=s_1\left( \frac{2}{3} \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}[/tex]

Answer: Price of a discount amision= Full Admission Price - discount Amount

Step-by-step explanation:

We have two variables "X" and "Y", where X= Full Admision Price and  Y= Discount Price of Admision  and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.

1) The reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is: Figures 1 and 3

How to find the transformation?

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

1) The reflection transformation is a mirror image of the original image.

Thus, the reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is:

Figures 1 and 3

[tex]\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}[/tex]

[tex]\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )[/tex]

The given expression is:

(cos 4θ + cos 2θ) / (cos 4θ - cos 2θ)

To simplify this expression, we can use the formula cot A sin C + cos B cos C = cot A sin B. Applying this formula gives us -cot 3θ cot θ as the simplified form of the expression.

Answer:

  $240

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]

Keri's monthly loan payment is $240 per month.

Answer: 300 per month

Step-by-step explanation:

Answer:

[tex]m(RS)=17[/tex] inches  (answer rounded to nearest tenths)

Step-by-step explanation:

Central angle there is 150 degrees.

The radius is 6.48 inches.

The formula for finding the arc length, RS, is

[tex]m(RS)=\theta \cdot r[/tex]

where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.

I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].

[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]

[tex]m(RS)=16.96[/tex] inches

Answer: [tex]17\ in[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Arc Lenght:

[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]

Where "r" is the radius and  "C" is the central angle of the arc in degrees.

You can identify in the figure that:

[tex]r=6.48\ in\\C=150\°[/tex]

Then, you can substitute values into the formula:

[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]

Rounded to the nearest tenth, you get:

[tex]Arc\ RS=17\ in[/tex]  

Answer:

15/2 x^2y - 5xy

Step-by-step explanation:

First find the area of the rectangle

A = l*w

   = 5xy * 2x

    10x^2y

The find the area of the triangle

A = 1/2 bh

   = 1/2 (5xy) (x+2)

   = 1/2((5x^2y + 10xy)

   = 5/2 x^2y +5xy

The shaded region is the area of the rectangle minus the area of the triangle

10x^2y -  (5/2 x^2y +5xy)

Distribute the minus sign

10x^2y -5/2 x^2y -5xy

Combining like terms by getting a common denominator

20/2x^2y -5/2 x^2y -5xy

15/2 x^2y - 5xy

The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).

To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.

The Quadratic Formula is given by:

x = √((-b ± √(b^2 - 4ac)) / (2a)).

Substitute the identified coefficients into the formula:

x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).

Simplify the expression:

x = √(((4 ± √(16 + 112)) / 8),

x = √(((4 ± √(128)) / 8),

x = √((4 ± 8√2) / 8).

Simplify further:

x = 1/2 ± √2.

Therefore, the correct answers are:

x = 1/2 + √2 and x = 1/2 - √2,

which corresponds to option (c).

Answer:

the area left to 51 on normal distribution curve

Step-by-step explanation:

we have to find the probability that at most 51 it means the probability of less than 51 . The probability of at most 51 or less than 51 on the normal distribution curve will be the area lest side of 51 for example if we have to find the are of at least 51 then the area on the normal distribution curve will be right of 51

so the answer will be the area left side of 51

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. To find the probability that at most 51 households have a gas stove, we convert the binomial random variable to a standard normal random variable and find the area to the left of 51 on the normal curve, which is extremely close to 0.

When the probability of a binomial random variable is approximated using the normal distribution, the area under the normal curve represents the probability of a certain range of values. In this case, we want to find the probability that at most 51 households have a gas stove. To do this, we need to find the area to the left of 51 on the normal curve.

To find this probability, we use the standard normal distribution table or a calculator. We convert the binomial random variable to a standard normal random variable using the formula z = (x - np) / √(npq), where x is the number of households, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, np = 500 * 0.2 = 100 and npq = 500 * 0.2 * 0.8 = 80. So, z = (51 - 100) / √80 ≈ -6.325.

Looking up this value in the standard normal distribution table, we find that the area to the left of -6.325 is extremely close to 0. Therefore, the probability that at most 51 households have a gas stove is approximately 0.

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Answer:

The actual price is 13.6 % lower than the expected price....

Step-by-step explanation:

Lets suppose the expected price = x

CPI = ( expected price ) : ( price in 1983 ) *100

219  =  ( x  : 12.95 ) *100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19*12.95

= $28.36  ( expected price )

p = ( 24.50*100 ) / 28.36

p= 2450/28.36

= 86.4 %

100 % - 86.4 % = 13.6 %

The actual price is 13.6 % lower than the expected price....

Answer:

c

Step-by-step explanation:

because i said so brudda

Answer:

  (2.31079, 6.83083)

Step-by-step explanation:

The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

Here, that means the new coordinates are ...

  (4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)

To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).

To rotate a point counterclockwise about the origin, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:

x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271

y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572

Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).

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Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve.  Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

       x - mean                              x - 75 bpm

z = ----------------- = -0.43073 = --------------------

       std. dev.                                    15

Thus,  x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

Answer:

  θ = 38°

Step-by-step explanation:

The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...

  sin(θ)/9 = sin(20°)/5

  sin(θ) = (9/5)sin(20°)

  θ = arcsin(9/5·sin(20°)) ≈ 38°

___

Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.

1. (3 + xz)(–3 + xz)

2. (y² – xy)(y² + xy)

3. (64y2 + x2)(–x2 + 64y2)

Explanation

The difference of 2 squares is in the form (a+b)(a-c).

(3 + xz)(–3 + xz) = (3 + xz)(xz -3)

                           = (xz + 3)(xz - 3)

                          = x²y²-3xy+3xy-9

                          =x²y² - 3²

(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²

                          = y⁴ - x²y²

(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)

                                      = 4096y⁴-64y²x²+64y²x²-x⁴

                                      = 4096y⁴ - x⁴

Answer:

  -3

Step-by-step explanation:

The average rate of change is the y-difference divided by the x-difference:

  (2 -14)/(6 -2) = -12/4 = -3

The average rate of change for the sequence is -3.

Answer:

-3

Step-by-step explanation:

Answer:

A. -3

Step-by-step explanation:

Answer:

Its undefined or D

Step-by-step explanation:

A undefined slope is something that is vertical or horizontal. The provided images explains it! Hope it helps!

Answer:

b.

Step-by-step explanation:

First off, let's name these endpoints.  We will call them J(3, -2) and K(8, 0).  The point we are looking for that divides this into a 3:1 ratio let's call L.  We are looking for point L that divides segment JK into a 3:1 ratio.

A 3:1 ratio means that we need to divide JK into 3 + 1 equal parts, or 4.  Point L divides JK into a 3:1 ratio.  We need to find the constant of proportionality, k, that can be used in the formula to find the coordinates of L.  k is found by putting the numerator of the 3/1 ratio over the sum of the numerator and denominator.  Therefore, our k value is 3/4.

Now we need to find the slope of the given segment.

[tex]m=\frac{0-(-2)}{8-3}=\frac{2}{5}[/tex]

The coordinates of L can be found in this formula:

[tex]L(x, y)=(x_{1}+k(run),x_{2}+k(rise))[/tex]

Filling in:

[tex]L(x,y)=(3+\frac{3}{4}(5),-2+\frac{3}4}(2))[/tex]

Simplifying we have:

[tex]L(x,y)=(3+\frac{15}{4},-2+\frac{6}{4})[/tex]

Simplifying further:

[tex]L(x,y)=(\frac{12}{4}+\frac{15}{4},\frac{-8}{4} +\frac{6}{4})[/tex]

And we have the coordinates of L to be

[tex]L(x,y)=(\frac{27}{4},-\frac{1}{2})[/tex]

27/4 does divide to 6.75

Hey There!

We'd distribute the negative sign first:

[tex]y + 7 = -x - 6[/tex]

Now, we'd have to isolate the variable y by subtracting seven in both sides:

[tex]y = -x - 13[/tex]

Replace y with f(x):

[tex]f(x) = -x - 13[/tex]

Our answer would be [tex]f(x) = -x - 13[/tex]

Answer:

f(x)-x-13

Step-by-step explanation:

Answer:

D. A stratified sample because the population is divided into separate groups and each group is randomly sampled.

Step-by-step explanation:

The researcher plans to take a random sample of 100 recent graduates of public universities and 100 recent graduates of private universities.

Her method is stratified sampling. This is because she divided the selected samples in two groups and will conduct the survey group wise.

These groups are also called strata.

Final answer:

Cluster sampling is used in the researcher's study design by dividing the population into clusters and randomly selecting all members from chosen clusters that is option A is correct.

Explanation:

Cluster sampling is utilized in the researcher's study design. In cluster sampling, the population is divided into separate clusters, and all subjects from a randomly selected cluster are selected. This method is practical when the population is dispersed geographically, making simple random sampling challenging.

The solution of the inequality is:

                       [tex]x\leq 3[/tex]

We are given a inequality in terms of variable x as:

[tex]2(4+2x)\geq 5x+5[/tex]

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

[tex]2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3[/tex]

The solution is:      [tex]x\leq 3[/tex]

Answer:

Option C.

Step-by-step explanation:

The given inequality is given as

2(4 + 2x) ≥ 5x + 5

8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]

Subtract 5 from each side of the inequality

(8 + 4x) - 5 ≥ (5x + 5) - 5

3 + 4x ≥ 5x

subtract 4x from each side of the inequality

(4x + 3) - 4x ≥ 5x - 4x

3 ≥ x

Or x ≤ 3

Option C. x ≤ 3 is the correct option.

Answer:

[tex]y = 6 + x[/tex]

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Assuming that the value of y is the total number of flour used in the mixture, then we would need to add both types of flour in order to find the value of y. Since we do not know the amount of white flour used, we will be substituting it for the variable x.

[tex]y = 6 + x[/tex]

The Equation above is stating that 6 cups of whole wheat flour added to the amount of white flour will equal the total amount of flour in the mixture.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

f(x) is an odd function and g(x) is an even function

Step-by-step explanation:

Even Function :

A function f(x) is said to be an even function if

f(-x) = f(x) for every value of x

Odd Function :

A Function is said to be an odd function if

f(-x)= -f(x)

Part a)

[tex]f(x)=x^3+x[/tex]

let us substitute x with -x

[tex]f(-x) = (-x)^3-x\\=-x \times -x \times -x\\=-x^3-x\\=-(x^3+x)\\=-f(x)[/tex]

Hence

f(-x)=-f(x)

There fore f(x) is an odd function

[tex]g(x)=x^2+1[/tex]

Substituting x with -x  we get

[tex]g(-x)=(-x)^2+1\\=-x \times -x+1\\=x^2+1\\=g(x)[/tex]

Hence g(-x)=g(x)

Therefore g(x) is an even Function.

Part b)

hf(x)=hx^3

Answer:

a. 8.4 km  b. 20 km/hr or 20,000 m/hr

Step-by-step explanation:

This is your polynomial:

[tex]d(v)=.004v^2+.2v+6[/tex]

The important thing to realize is that d(v) is the distance it takes for the boat to stop.  That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.

For part a. we are looking for d(v), the stopping distance, when v = 10.  That means that we will sub in a 10 for each v in the function and solve for d(v):

[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so

d(10) = 8.4 km

Now comes the part I was referring to above.  Part b is asking us the speed of the boat if it takes 11.6 meters to stop.  If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:

[tex]11.6=.004v^2+.2v+6[/tex]

The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.  

[tex]0=.004v^2+.2v-5.6[/tex]

Plugging that into the quadratic formula gives you 2 values of velocity:

v = 20 km/hr and -70 km/hr

We all know that neither time nor distance in math will EVER be negative so we can discount the negative number.  However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.

Answer:

Step-by-step explanation:

Part A:

The solution of a system is not just the x coordinates; it is the whole coordinate pair that is the solution, where both x and y are the same.  Normally, when you have a system and are solving them simultaneously, you are looking for the point at which they are equal.  This is a very useful concept in business and finance, both in the home for personal information, and in the office setting where companies are.  Where the 2 equations intersect is a point where they are equal.  

Part B:

The graphs do not intersect right at a perfect integer of x.  Therefore, we will solve these equations simultaneously to solve first for x, then we will plug in x to solve for y.  Since we have the equations set to equal each other, we can solve for x by getting everything on one side of the equation and then setting it equal to 0.  

2 - x = 4x + 3 so

5x + 1 = 0.  Solving for x,

5x = -1 so

[tex]x=-\frac{1}{5}[/tex]

The y coordinate can be found by subbing in this value of x into either equation.  If y = 2 - x, and x = -1/5, then

y = 2 -(-1/5) and y = 2 + 1/5 and y = 10/5 + 1/5 gives us that y = 11/5

Thus, the coordinate pair that is the solution to that system is

[tex](-\frac{1}{5},\frac{11}{5})[/tex]

Part C:

You would solve the system graphically by graphing both lines on the same window.  However, since their intersection is not an integer pair, but are fractions, you would not be able to tell EXACTLY where they intersect.  From the graphing window, you would hit your 2nd button then "trace" which is in the row at the very top of the buttons below the window.  Then hit 5:  intersect.  You'll be back to your graph of the lines, and there will be a cursor blinking along the line you graphed under Y1.  Move the cursor til it is right over the intersection of the lines and hit "enter".  Then you'll be back to the graphs with a blinking cursor over the line you entered in Y2.  Move that cursor along the line til it is dead-center over the other point on the first line and hit "enter" again.  At the bottom, you will see the x and y coordinates that are the intersection of this system.

Answer:

GLH is congruent to JLK as the quadrilateral is a parallelogram,

KJ = GH OR HJ = GK

GL = LJ OR. HL = LK

triangle JKG = GHJ

triangle HGK = KJH

Answer:

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...

Answer:

  18°

Step-by-step explanation:

The law of cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.

  cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140

  A = arccos(133/140) ≈ 18.2° ≈ 18°